Most motion compensation methods dealt with in the literature make strong assumptions about the smoothness of the underlying motion eld. For instance, block-matching algorithms assume a blockwise-constant motion eld and are adequate under translational motion models; triangle motion compensation assumes a piecewise-planar motion eld, and this model captures zooming, warping and rotational motio...

Recent discoveries in differential topology are reviewed in light of their possible implications for spacetime models and related subjects in theoretical physics. Although not often noted, a particular smoothness (differentiability) structure must be imposed on a topological manifold before geometric or other structures of physical interest can be discussed. The recent discoveries of interest h...

The Indiana Department of Transportation (INDOT) is currently utilizing a profilograph and the profile index for measuring smoothness assurance for newly constructed pavements. However, there are benefits to implementing a new International Roughness Index (IRI)–based smoothness specification utilizing road profiles measured using inertial profilers. Technological advancements have improved the...

In this paper the smoothness properties of Green’s operator-function an exponentially dichotomous bilinear matrix system and the smoothness properties the invariant torus of nonhomogeneus matrix system of equations have been considered. It hHave been proved that if some conditions, concerning the properties of coefficient of the system hold this operator-function has smoothness index which depe...

We consider infinitely dimensional classes of functions and instead the relative error setting, which was used in previous papers on integral norm discretization, we absolute setting. demonstrate how known results from two areas research – supervised learning theory numerical integration can be sampling discretization square different function classes. prove a general result, shows that sequenc...